3366 papers
Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.
On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.
This paper rigorously derives the physical gauge group of Yang-Mills theory as the quotient of boundary-preserving gauge transformations by Gauss law transformations by analyzing the structure of the instantaneous state space, and extends this analysis to demonstrate how boundary conditions and the resulting gauge group differ between the unbroken and broken phases of Yang-Mills-Higgs theory.
This paper establishes a prequantum bundle structure over the space of codimension-2 submanifolds by using complex-valued implicit representations, thereby offering a new geometric interpretation of the Marsden-Weinstein symplectic structure as the curvature of a connection form that measures the average volume swept by phase level set deformations.
This perspective paper reviews the application of Moreau-Yosida regularization in density-functional theory, highlighting its role in reformulating the Kohn-Sham approach, enabling density-potential inversion, and linking the theory to classical field theories, while outlining future development opportunities.
This paper analyzes a model of conducting fluid filtration through a porous layer composed of spherical cells with porous cores and liquid shells, deriving a priori estimates that prove the boundedness of velocity, pressure, electric potential, and ion flux densities while characterizing their dependence on the Debye radius.
This study combines micromagnetic simulations and analytical modeling to reveal how the internal structural imbalance of skyrmioniums drives a finite Hall effect and diverse current-induced instability pathways, while also characterizing the rich collective dynamics of skyrmionium-based meta-matter for potential applications in tunable nonequilibrium topological systems.
This paper presents a rigorous algebraic framework to systematically characterize the asymptotic behavior and dispersion of all types of multi-block degeneracies in non-Hermitian systems under perturbations, offering a practical tool for analyzing complex experimental scenarios.
This paper constructs two inequivalent noncommutative quantum field theories on -Minkowski space using the Batalin-Vilkovisky formalism, demonstrating that a braided -algebra approach yields standard logarithmic divergences without UV/IR mixing, while a classical -algebra approach exhibits a periodic form of UV/IR mixing characterized by non-analyticity on an infinite lattice of exceptional momenta.
This paper establishes a universal finite- framework for Wilson loop expectations in lattice Yang-Mills theory across any dimension and gauge group , revealing that their state-sum expansion factorizes into action-dependent weights and action-independent topological coefficients that can be analyzed through gauge/string expansions, spin-foam models, and master loop equations.
This paper presents a dimension-independent, basis-agnostic closed-form exponential unitary transformation that maps any two pure quantum states using a single generator, eliminating the need for explicit basis constructions required by previous methods.
This paper demonstrates that factorizing differential equations with respect to nonlocal pseudosymmetries yields Bäcklund transformations, which are interpreted as nonlocal -morphisms determined by the basic invariants of those symmetries.